Why did the framers wanted to have majority rule but also protect the rights of the minority?

The framers wanted to have majority rule because it is the basic principle of democracy.

Democracy is a system where people vote to elect their governors, and the majority votes win, in democracy the majority of people have the power to decide which candidate wins. So without majority rule there would not be democracy.

The framers also wanted to protect the rights of the minority to prevent that a majority rule would lead to abuse of power and oppress the minority. The Bill of Rights written by James Madison protects the minority rights in the Constitution, so the majority has to respect those basic rights when passing laws and making decisions and the minority has the power to someday become the majority, making democracy work.